Math Problem Statement

What is the variance of the​ stock's returns? Var(R) = 1/4-1 x [(-0.0455-0.1033)^2+(0.2852-0.1033)^2+(0.1261-0.1033)^2+(0.0473-0.1033)^2] The variance of the​ stock's returns is enter your response here. ​(Round to five decimal​ places.)

Solution

as np

Given values for the calculation

returns = [-0.0455, 0.2852, 0.1261, 0.0473] mean_return = 0.1033

Variance formula calculation

variance = (1 / (4 - 1)) * sum((x - mean_return) ** 2 for x in returns)

Round to five decimal places

variance_rounded = round(variance, 5) The variance of the stock's returns is 0.01963.

Would you like a detailed explanation or have any questions? Here are some related questions to deepen your understanding:

  1. How is variance used to measure the risk of a stock's returns?
  2. What is the difference between variance and standard deviation in financial contexts?
  3. How would the variance change if additional data points were added?
  4. Can you explain why dividing by n1n-1 (instead of nn) is used in this calculation?
  5. How does the mean return affect the calculation of variance?

Tip: Variance provides a good measure of dispersion but interpreting it alongside the mean return is crucial for investment decisions.

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Math Problem Analysis

Mathematical Concepts

Statistics
Variance Calculation
Mean and Dispersion

Formulas

Variance = (1 / (n - 1)) × Σ(x_i - mean)^2

Theorems

Central Limit Theorem (implicitly relevant when interpreting statistical measures)

Suitable Grade Level

Grades 10-12